Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections

Kerala State Board New Syllabus Plus One Maths Chapter Wise Previous Questions and Answers Chapter 11 Conic Sections.

Kerala Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections

Plus One Maths Conic Sections 3 Marks Important Questions

Question 1.
1. Find the equation of the Hyperbola where foci (0,±8)are and the length of the latus rectum is 24.(IMP-2012)
Answer:
Since foci (0,±8)
=> ae = 8
Latus rectum = 24= \(\frac {2b² }{ a }\)
=> 12a = b²
b² =a²(e² -1)
=> b² – a²e² -a²
=>12a = 64 – a²
=>a²+12a-64 = 0
=> a = – 16,4
acceptable value is => a = 4
=> 48 = b²
Hence equation is
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 1

Question 2.
Find the equation of the circle with centre (- a,- b)and radius \(\sqrt{a^{2}+b^{2}}\) . (IMP-2012)
Answer:
We have the equation of a circle as;
(x-h)² + (y-k)² – r²
=> (x + a)² +(y + b)² = a² + b²
=> x² +2 ax + a² + y² +2 by + b² =a² +b²
=> x² +2ax + y² +2by = 0

Question 3.
Find the coordinate of the foci, the length of the major axis, minor axis, latus rectum and eccentricity of the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\) . (MARCH-2013)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 2

Question 4.
Consider the parabola y² =12x. (MARCH-2015)
i) Find the coordinate of the focus.
ii) Find the length of the latus rectum.
Answer:
i) Given; y² =12x comparing with y² = 4ax We have 4a = 12 => a = 3 Then; Focus is (3,0)
ii) Length of latus rectum = 4a = 12

Question 5.
Find the foci, vertices, the eccentricity and the length of the latus rectum of the hyperbola 16x² – 9y² =144. (SAY-2017) 
Answer:
The equation of the hyperbola is of the form
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 3
=>a² =9,b² =16
=>c² = a² +b² =9 + 16 = 25
=>c = 5
Coordinate of foci are (±5,0)
Coordinate of vertices are (±a,0) => (±3,0)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 4

Question 6.
Directrix of the parabola x² = – 4ay is ……….. (MARCH-2014)
a) x + a = 0
b) x – a = 0
c) y – a = 0
d) y + a = 0
Find the equation of the ellipse whose length of the major axis is 20 and foci are (0 ±5)
(March-2015)
Answer:
i) y-a = 0
ii) The equation of the ellipse is of the form;
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 5

Question 7.
Find the coordinates of the focii, vertices, eccentricity and the length of the Latus Rectum of the ellipse 100x² + 25y² = 2500 (IMP-2015)
Answer:
Given: 100x² +25y² = 2500
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 6

Question 8.
Find the foci, vertices, length of the major axis and eccentricity of the ellipse: \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\) (MARCH-2016)
Answer:
Since 25 > 9 the standard equation of the ellipse is \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\) => a² =25;b² =9
c² =a² – b² =25 – 9 = 16
=>c = 4
Coordinate of foci are (±4,0)
Coordinate of vertex are (±5,0)
Length of major axis = 2a = 2 x 5 = 10
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 7

Plus One Maths Conic Sections 4 Marks Important Questions

Question 1.
An ellipse whose major axis as x-axis and the centre (0,0) passes through (4,3) and (- 1,4). (MARCH-2010)
i) Find the equation of the ellipse.
ii) Find is eccentricity.
Answer:
i)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 8
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 9

Question 2.
Consider the conic find 9y² -4x² = 36 (IMP-2010)
i) The foci.
ii) Eccentricity.
iii) Length of latus rectum.
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 10

Question 3.
Find the equation of the circle with center (2,2) and passing through the point (4,5). (MARCH-2011)
Find the eccentricity and the length of latus rectum of the ellipse 4x² + 9y² =36
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 11

Question 4.
For the hyperbola 9x² – 16y² =144 (IMP-2011)
i) find eccentricity.
ii) find the latus rectum.
Answer:
i)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 12
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 13

Question 5.
A hyperbola whose transverse axis is x-axis, centre (0,0) and foci (±√10,0) passes through the point (3,2) (MARCH-2012)
i) Find the equation of the hyperbola.
ii) Find the eccentricity.
Answer:
i)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 14
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 15

Question 6.
Find the centre and radius of the circle. (IMP-2013)
x² +y² – 8x + 10y – 12 = 0.
ii) Determine the eccentricity and length of latus rectum of the hyperbola —–
Answer:
i) Comparing with the general equation we have
g = – 4; f = 5; c = – 12
Centre – (- g,- f) => (4,- 5)
\(\sqrt{g^{2}+f^{2}-c} \)= \(\sqrt{16+25+12}=\sqrt{53}\)
ii)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 16

Question 7.
Consider the ellipse \(\frac{x^{2}}{25}+\frac{y^{2}}{9}=1\). Find the coordinate of the foci, the length of the major axis, the length of the minor axis, latus rectum and eccentricity. (MARCH-2014)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 17

Question 8.
Which one of the following equations (IMP-2014)
represents a parabola which is symmetrical about the positive Y-axis?
a) y² = 4x
b) y² = – 8x
c) x² + 4y = 0
d) x² – 4y = 0
ii) Find the equation of the ellipse vertices are (±13,0) and foci are (±5,0)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 18

Question 9.
Match the following. (IMP-2014)
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 19
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 20

Question 10.
i) Find the equation of the parabola with focus (6,0) and equation of the directrix is x = – 6. (MARCH-2017)
ii) Find the coordinate of the foci, vertices, the length of transverse axis, conjugate axis and eccentricity of the hyperbola \(\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\)
(MARCH -2017)
Answer:
Plus One Maths Chapter Wise Previous Questions Chapter 11 Conic Sections 21

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